| The safety of the whole power system is related to the stable operation of the hydro-generator system, so hydro-generator kinetics characteristics are the key factor which we need to consider during designing and building. The problem of the simulation of hydro-generator system is complex since a force field and an electromagnetic field is coupled. If we directly make a numerical simulation with coupling field, the process in modeling and calculation is complicated. In order to make an easy calculation, we usually regard the action of magnetic field on rotor as an unbalanced magnetic pull (UMP).We consider a rotor system which has four degrees of freedom and contains the effects of rotary inertia, gyroscopic moments, the resistance outside the shaft, eccentric mass and the unbalanced magnetic pull. The dynamics equation of this system is: (?)In this equationm is the quality of the disk, k ij , cij(i ,j=1,L4)is elastic coefficients and damping coefficients, respectively, H is the gyroscopic moment, e is the eccentricity, J d is the moment of inertia about its diameter, Fx UMP, F yUMPare the unbalanced magnetic pull in X and Y directions, respectively. According to the theory of electromagnetism, the Maxwell stress in the boundary of air gap of the rotor is given by: (?) Where B =Λ(α, t ) F (α,t) is flux density of the air gap,Λ(α,t) is air gap permeance , F (α,t) is the fundamental magneto-motive force (MMF) of the air gap,μ0 is the air permeance. The air gap permeance is expressed as a Fourier series: (?)The fundamental MMF of the air gap in a three-phrase generator under no-load state can be expressed as (?)Where Fr is the amplitude of the fundamental MMF of the excitation current of the rotor.Then the UMP can be calculated by using the Maxwell stress around the rotor surface and integration. When the number of pole pairs is more than 3 and the terms to order 3 are kept for Taylor expansion: (?)Commercial ANSYS is finite element software which is widely used in engineering. If we directly make a numerical simulation with coupling field by ANSYS, the process in modeling and calculation is very complicated. Therefore, we make settings and adjustments to the nonlinear spring element COMBIN39 to simulate the nonlinear unbalanced magnetic pull imposed on the rotor. Then we use BEAM188 element to simulate the shaft of the rotor and build the finite element model of the rotor. We finally carry out a nonlinear transient dynamic analysis. A simple generator model and a complex hydro-generator from a power plant are adopted in this paper. We calculate the transient dynamics response of the mechanical and electromagnetic coupling for the model and the hydro-generator subjected to the UMP and eccentric mass force. In the meanwhile, we get the response tracks for the different amplitude of the fundamental MMF which will indicate the influence of the unbalanced magnetic pull imposing to the rotor system.From the numerical results we can get the following conclusions: 1.ANSYS numerical simulation results and self-made Fortran numerical simulation results are almost identical; 2. Compared to the steady state orbits without nonlinear magnetic pull, the UMP make the radius of the orbits increased along with amplitude of the fundamental MMF increasing; 3.The maximum displacement obtained in transient response may be larger than the radius of steady state orbits, this requires full consideration in design process.
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